Approximation Of Additive Convolution-Like Operators
Didenko, Victor; Silbermann, Bernd
ISBN 10: 3764387505 ISBN 13: 9783764387501
Published by Birkhäuser, 2008
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Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated – and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory. However,invariousapplicationsthereoftenarisecontinuousoperatorsacting on complex Banach spaces that are not linear but only additive – i. e. , A(x+y)= Ax+Ay for all x,y from a given Banach space. It is easily seen that additive operators 1 are R-linear provided they are continuous.
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Title: Approximation Of Additive Convolution-Like ...
Publisher: Birkhäuser
Publication Date: 2008
Binding: Soft cover
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Condition: Sehr gut. Zustand: Sehr gut | Seiten: 324 | Sprache: Englisch | Produktart: Bücher | Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated ¿ and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory. However,invariousapplicationsthereoftenarisecontinuousoperatorsacting on complex Banach spaces that are not linear but only additive ¿ i. e. , A(x+y)= Ax+Ay for all x,y from a given Banach space. It is easily seen that additive operators 1 are R-linear provided they are continuous. Seller Inventory # 4144046/12
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Based on algebraic techniquesFirst book entirely devoted to numerical analysis for additive operatorsCovers various aspects of approximation methods for equations with conjugation arising in the boundary integral equation methodFirst. Seller Inventory # 5279931
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Approximation of Additive Convolution-Like Operators
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Birkhäuser, Birkhäuser Mai 2008, 2008
ISBN 10: 3764387505
ISBN 13: 9783764387501
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book deals with numerical analysis for certain classes of additive operators and related equations, including singular integral operators with conjugation, the Riemann-Hilbert problem, Mellin operators with conjugation, double layer potential equation, and the Muskhelishvili equation. It is the first book to present systematic study of approximation methods for the Muskhelishvili equation, and the first book entirely devoted to numerical analysis for additive operators. The authors propose a unified approach to the analysis of the approximation methods under consideration based on special real extensions of complex C\*-algebras. The list of the methods considered includes spline Galerkin, spline collocation, qualocation, and quadrature methods. The book is self-contained and accessible to graduate students.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 324 pp. Englisch. Seller Inventory # 9783764387501
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